Firstly, the barrel was finished bright on purpose. Many period guns were polished bright and many were blued. Browning began to be more common at the tail end of the 18th century, but would look off on that rifle, in my opinion. I wouldn’t touch the finish, but if you choose to, get some advice from folks who are well-versed in period metal finishes like fire bluing, etc..
For the bore (disclaimer: there are a 1,001 ways to clean a rifle, this is just one simple opinion). If it was my rifle, I would start simple with the bore and simply scrub it with some wet patches and then some dry patches to get a good feel for how much rust you are actually dealing with. If it’s just a little surface rust, scrub with oil-saturated patches with something like Breakfree and you might take care of it. You can use some cut up scotchbrite pad/bronze wool/brass brush as a mild abrasive if necessary, if you can actually feel the rusty spots as your wiping. Even if there is a little bit of surface rust left, you can probably take care of the remaining rust by shooting some patched balls out of it. Follow that up with a good cleaning, drying and oiling.
If the rust is more substantial and you have pitting in the bore, then the answer will be different. Post your findings and folks can chime in accordingly.
